Using Motion, Energy, and Fourier Methods to Analyze Price Series
Summary
The document proposes borrowing concepts from physics to describe market fluctuations. It suggests measuring price movement as velocity, with possible measures based on accumulated absolute changes, net changes, or the difference between two observations. It then extends the analogy to acceleration and to kinetic energy, treating traded volume as a possible proxy for mass. These quantities are presented as ways to characterize volatility or market activity, rather than as validated trading signals.
It also recommends Fourier analysis to decompose a time series into wave-like components, with the possibility of forecasting while those components remain useful. The author notes that this approach can be computationally difficult and that the duration of the modeled waves must be assessed. As a separate connection, the answer observes that the Black–Scholes option-pricing equation resembles a heat-diffusion equation. The document offers suggestions rather than empirical tests: it reports no forecasting results, specifies no calibration procedure, and does not establish that the physical analogies predict returns or improve trading decisions.
Key ideas
- Price changes can be summarized as movement over time using several definitions of distance traveled.
- Acceleration and volume-weighted kinetic energy are proposed as additional descriptions of market activity.
- Fourier decomposition may reveal wave-like components that could support forecasts while they persist.
- The duration of any modeled wave and the computational cost of Fourier methods are practical limitations.
- The Black–Scholes equation is linked conceptually to the physics of heat diffusion.
Tags
Full text
# How to use physics models in Time Series Analysis and Forecasting. # How to use physics models in Time Series Analysis and Forecasting. I have been studying methods of Technical Analysis for several years and I am disappointed. I actually do not consider it useful. I have not met anyone who can constantly win in the market using these technics. Right now I am more lining towards methods derived from physics and here comes my questions. Do you know some methods which can be considered as indicators for measuring market fluctuations and “the heat”? Is this approach worth investigating? ## Answer by Robert Szóstakowski (score 5, accepted) https://quant.stackexchange.com/a/20653 I am not a physicist, but I thought about some approaches based on physics several months ago. Some of them are easy to implement and some are really hard. The list below is made from the easiest method to the hardest: - You can start from the basic physics of the movement and measure the velocity of the time series ( based on v = road/ time). You can calculate road using different approaches: a) Using a sum of absolute values of returns or price changes. b) Using a sum of returns or price changes. c) Compare price changes between point A and B in time series. It will give you some kind of volatility indicator for the time series. - Then you can analyze the road - s (from the equation s = 0.5*a *t^2) using a model with acceleration - Moreover, you can measure the “kinetic energy” of the time series using the equation E_kin = 0.5 * m* v^2 where mass can be considered as the volume of the security. - You can use the Fourier transformation https://en.wikipedia.org/wiki/Fourier_transform and try to decompose the time series into a series of wavelets. This might be very hard computationally . In this case you need to analyze how to predict how long this wavelet models will last in time. An advantage of this approach is the fact that you can make a forecast when you have the model calculated. - Lastly, there is a lot of methods for derivative pricing based on physics. For example the most popular model for options pricing – the Black Scholes model is based on the equation which is identical to the heat diffusion equation.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.